Package edu.jas.ps

Class MultiVarPowerSeriesRing<C extends RingElem<C>>

java.lang.Object

edu.jas.ps.MultiVarPowerSeriesRing<C>

Type Parameters:

C - ring element type

All Implemented Interfaces:

AbelianGroupFactory<MultiVarPowerSeries<C>>, ElemFactory<MultiVarPowerSeries<C>>, MonoidFactory<MultiVarPowerSeries<C>>, RingFactory<MultiVarPowerSeries<C>>, java.io.Serializable

public class MultiVarPowerSeriesRing<C extends RingElem<C>>
extends java.lang.Object
implements RingFactory<MultiVarPowerSeries<C>>

Multivariate power series ring implementation. Uses lazy evaluated generating function for coefficients.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
RingFactory<C>	coFac	Coefficient ring factory.
static int	DEFAULT_TRUNCATE	Default truncate.
ExpVector	EVZERO	Zero ExpVector.
int	nvar	The number of variables.
MultiVarPowerSeries<C>	ONE	The constant power series 1 for this ring.
protected static java.util.Random	random	A default random sequence generator.
protected java.lang.String[]	vars	The names of the variables.
MultiVarPowerSeries<C>	ZERO	The constant power series 0 for this ring.

Constructor Summary

Constructors

Constructor	Description
MultiVarPowerSeriesRing(GenPolynomialRing<C> fac)	Constructor.
MultiVarPowerSeriesRing(RingFactory<C> coFac, int nv)	Constructor.
MultiVarPowerSeriesRing(RingFactory<C> coFac, int nv, int truncate)	Constructor.
MultiVarPowerSeriesRing(RingFactory<C> cofac, int nv, int truncate, java.lang.String[] names)	Constructor.
MultiVarPowerSeriesRing(RingFactory<C> cofac, int nv, java.lang.String[] names)	Constructor.
MultiVarPowerSeriesRing(RingFactory<C> coFac, java.lang.String[] names)	Constructor.

Method Summary

Modifier and Type	Method	Description
java.math.BigInteger	characteristic()	Characteristic of this ring.
MultiVarPowerSeries<C>	copy(MultiVarPowerSeries<C> c)	Copy power series.
boolean	equals(java.lang.Object B)	Comparison with any other object.
MultiVarPowerSeries<C>	fixPoint(MultiVarPowerSeriesMap<C> map)	Fixed point construction.
MultiVarPowerSeries<C>	fromInteger(long a)	Get a (constant) MultiVarPowerSeries<C> from a long value.
MultiVarPowerSeries<C>	fromInteger(java.math.BigInteger a)	Get a (constant) MultiVarPowerSeries<C> from a java.math.BigInteger.
MultiVarPowerSeries<C>	fromPolynomial(GenPolynomial<C> a)	Get a MultiVarPowerSeries<C> from a GenPolynomial<C>.
java.util.List<MultiVarPowerSeries<C>>	fromPolynomial(java.util.List<GenPolynomial<C>> A)	Get a list of MultiVarPowerSeries<C> from a list of GenPolynomial<C>.
MultiVarPowerSeries<C>	fromPowerSeries(UnivPowerSeries<C> ps, int r)	Get a MultiVarPowerSeries<C> from a univariate power series.
MultiVarPowerSeries<C>	generate(java.util.function.Function<ExpVector,C> gener)	Generate a power series via lambda expression.
java.util.List<MultiVarPowerSeries<C>>	generators()	Get a list of the generating elements.
MultiVarPowerSeries<C>	getCOS(int r)	Get the power series of the cosinus function.
MultiVarPowerSeries<C>	getEXP(int r)	Get the power series of the exponential function.
MultiVarPowerSeries<C>	getONE()	Get the one element.
MultiVarPowerSeries<C>	getSIN(int r)	Get the power series of the sinus function.
MultiVarPowerSeries<C>	getTAN(int r)	Get the power series of the tangens function.
java.lang.String[]	getVars()	Get the variable names.
MultiVarPowerSeries<C>	getZERO()	Get the zero element.
int	hashCode()	Hash code for this .
boolean	isAssociative()	Query if this ring is associative.
boolean	isCommutative()	Query if this ring is commuative.
boolean	isField()	Query if this ring is a field.
boolean	isFinite()	Is this structure finite or infinite.
MultiVarPowerSeries<C>	parse(java.io.Reader r)	Parse a power series.
MultiVarPowerSeries<C>	parse(java.lang.String s)	Parse a power series.
GenPolynomialRing<C>	polyRing()	Get the corresponding GenPolynomialRing<C>.
MultiVarPowerSeries<C>	random()	Generate a random power series with k = 5, d = 0.7.
MultiVarPowerSeries<C>	random(int k)	Generate a random power series with d = 0.7.
MultiVarPowerSeries<C>	random(int k, float d)	Generate a random power series.
MultiVarPowerSeries<C>	random(int k, float d, java.util.Random rnd)	Generate a random power series.
MultiVarPowerSeries<C>	random(int k, java.util.Random rnd)	Generate a random power series with d = 0.7.
MultiVarPowerSeries<C>	seriesOfTaylor(TaylorFunction<C> f, java.util.List<C> a)	Taylor power series.
int	setTruncate(int t)	Set truncate.
MultiVarPowerSeries<C>	solvePDE(MultiVarPowerSeries<C> f, C c, int r)	Solve an partial differential equation. y_r' = f(y_r) with y_r(0) = c.
java.lang.String	toScript()	Get a scripting compatible string representation.
java.lang.String	toString()	To String.
int	truncate()	Truncate.
java.lang.String	varsToString()	Get a String representation of the variable names.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface edu.jas.structure.ElemFactory

valueOf

Field Detail

random

protected static final java.util.Random random

A default random sequence generator.

DEFAULT_TRUNCATE

public static final int DEFAULT_TRUNCATE

Default truncate.

See Also:

Constant Field Values

EVZERO

public final ExpVector EVZERO

Zero ExpVector.

coFac

public final RingFactory<C extends RingElem<C>> coFac

Coefficient ring factory.

nvar

public final int nvar

The number of variables.

vars

protected java.lang.String[] vars

The names of the variables. This value can be modified.

ONE

public final MultiVarPowerSeries<C extends RingElem<C>> ONE

The constant power series 1 for this ring.

ZERO

public final MultiVarPowerSeries<C extends RingElem<C>> ZERO

The constant power series 0 for this ring.

Constructor Detail

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(GenPolynomialRing<C> fac)

Constructor.

Parameters:

fac - polynomial ring factory.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> coFac,
                               int nv)

Constructor.

Parameters:

coFac - coefficient ring factory.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> coFac,
                               int nv,
                               int truncate)

Constructor.

Parameters:

coFac - coefficient ring factory.

truncate - index of truncation.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> coFac,
                               java.lang.String[] names)

Constructor.

Parameters:

coFac - coefficient ring factory.

names - of the variables.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> cofac,
                               int nv,
                               java.lang.String[] names)

Constructor.

Parameters:

cofac - coefficient ring factory.

nv - number of variables.

names - of the variables.

MultiVarPowerSeriesRing

public MultiVarPowerSeriesRing(RingFactory<C> cofac,
                               int nv,
                               int truncate,
                               java.lang.String[] names)

Constructor.

Parameters:

cofac - coefficient ring factory.

truncate - index of truncation.

names - of the variables.

Method Detail

fixPoint

public MultiVarPowerSeries<C> fixPoint(MultiVarPowerSeriesMap<C> map)

Fixed point construction.

Parameters:

map - a mapping of power series.

Returns:

fix point wrt map.

toString

public java.lang.String toString()

To String.

Overrides:

toString in class java.lang.Object

Returns:

string representation of this.

varsToString

public java.lang.String varsToString()

Get a String representation of the variable names.

Returns:

names separated by commas.

getVars

public java.lang.String[] getVars()

Get the variable names.

Returns:

names.

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<C extends RingElem<C>>

Returns:

script compatible representation for this ElemFactory.

See Also:

ElemFactory.toScript()

equals

public boolean equals(java.lang.Object B)

Comparison with any other object.

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this .

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

getZERO

public MultiVarPowerSeries<C> getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<C extends RingElem<C>>

Returns:

0 as MultiVarPowerSeries.

getONE

public MultiVarPowerSeries<C> getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<C extends RingElem<C>>

Returns:

1 as MultiVarPowerSeries.

generators

public java.util.List<MultiVarPowerSeries<C>> generators()

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<C extends RingElem<C>>

Returns:

list of generators for the algebraic structure.

See Also:

ElemFactory.generators()

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

isFinite in interface ElemFactory<C extends RingElem<C>>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

truncate

public int truncate()

Truncate.

Returns:

truncate index of power series.

setTruncate

public int setTruncate(int t)

Set truncate.

Parameters:

t - new truncate index.

Returns:

old truncate index of power series.

getEXP

public MultiVarPowerSeries<C> getEXP(int r)

Get the power series of the exponential function.

Parameters:

r - variable for the direction.

Returns:

exp(x_r) as MultiVarPowerSeries.

getSIN

public MultiVarPowerSeries<C> getSIN(int r)

Get the power series of the sinus function.

Parameters:

r - variable for the direction.

Returns:

sin(x_r) as MultiVarPowerSeries.

getCOS

public MultiVarPowerSeries<C> getCOS(int r)

Get the power series of the cosinus function.

Parameters:

r - variable for the direction.

Returns:

cos(x_r) as MultiVarPowerSeries.

getTAN

public MultiVarPowerSeries<C> getTAN(int r)

Get the power series of the tangens function.

Parameters:

r - variable for the direction.

Returns:

tan(x_r) as MultiVarPowerSeries.

solvePDE

public MultiVarPowerSeries<C> solvePDE(MultiVarPowerSeries<C> f,
                                       C c,
                                       int r)

Solve an partial differential equation. y_r' = f(y_r) with y_r(0) = c.

Parameters:

f - a MultiVarPowerSeries.

c - integration constant.

r - variable for the direction.

Returns:

f.integrate(c).

isCommutative

public boolean isCommutative()

Query if this ring is commuative.

Specified by:

isCommutative in interface MonoidFactory<C extends RingElem<C>>

Returns:

true, if this ring is commutative, else false.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<C extends RingElem<C>>

Returns:

true if this ring is associative, else false.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<C extends RingElem<C>>

Returns:

true if this ring is a field, else false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<C extends RingElem<C>>

Returns:

characteristic of this ring.

fromInteger

public MultiVarPowerSeries<C> fromInteger(long a)

Get a (constant) MultiVarPowerSeries<C> from a long value.

Specified by:

fromInteger in interface ElemFactory<C extends RingElem<C>>

Parameters:

a - long.

Returns:

a MultiVarPowerSeries<C>.

fromInteger

public MultiVarPowerSeries<C> fromInteger(java.math.BigInteger a)

Get a (constant) MultiVarPowerSeries<C> from a java.math.BigInteger.

Specified by:

fromInteger in interface ElemFactory<C extends RingElem<C>>

Parameters:

a - BigInteger.

Returns:

a MultiVarPowerSeries<C>.

polyRing

public GenPolynomialRing<C> polyRing()

Get the corresponding GenPolynomialRing<C>.

Returns:

GenPolynomialRing<C>.

fromPolynomial

public MultiVarPowerSeries<C> fromPolynomial(GenPolynomial<C> a)

Get a MultiVarPowerSeries<C> from a GenPolynomial<C>.

Parameters:

a - GenPolynomial<C>.

Returns:

a MultiVarPowerSeries<C>.

fromPolynomial

public java.util.List<MultiVarPowerSeries<C>> fromPolynomial(java.util.List<GenPolynomial<C>> A)

Get a list of MultiVarPowerSeries<C> from a list of GenPolynomial<C>.

Parameters:

A - list of GenPolynomial<C>.

Returns:

a list of MultiVarPowerSeries<C>.

fromPowerSeries

public MultiVarPowerSeries<C> fromPowerSeries(UnivPowerSeries<C> ps,
                                              int r)

Get a MultiVarPowerSeries<C> from a univariate power series.

Parameters:

ps - UnivPowerSeries<C>.

r - variable for the direction.

Returns:

a MultiVarPowerSeries<C>.

random

public MultiVarPowerSeries<C> random()

Generate a random power series with k = 5, d = 0.7.

Returns:

a random power series.

random

public MultiVarPowerSeries<C> random(int k)

Generate a random power series with d = 0.7.

Specified by:

random in interface ElemFactory<C extends RingElem<C>>

Parameters:

k - bit-size of random coefficients.

Returns:

a random power series.

random

public MultiVarPowerSeries<C> random(int k,
                                     java.util.Random rnd)

Generate a random power series with d = 0.7.

Specified by:

random in interface ElemFactory<C extends RingElem<C>>

Parameters:

k - bit-size of random coefficients.

rnd - is a source for random bits.

Returns:

a random power series.

random

public MultiVarPowerSeries<C> random(int k,
                                     float d)

Generate a random power series.

Parameters:

k - bit-size of random coefficients.

d - density of non-zero coefficients.

Returns:

a random power series.

random

public MultiVarPowerSeries<C> random(int k,
                                     float d,
                                     java.util.Random rnd)

Generate a random power series.

Parameters:

k - bit-size of random coefficients.

d - density of non-zero coefficients.

rnd - is a source for random bits.

Returns:

a random power series.

generate

public MultiVarPowerSeries<C> generate(java.util.function.Function<ExpVector,C> gener)

Generate a power series via lambda expression.

Parameters:

gener - lambda expression.

Returns:

a generated power series.

copy

public MultiVarPowerSeries<C> copy(MultiVarPowerSeries<C> c)

Copy power series.

Specified by:

copy in interface ElemFactory<C extends RingElem<C>>

Parameters:

c - a power series.

Returns:

a copy of c.

parse

public MultiVarPowerSeries<C> parse(java.lang.String s)

Parse a power series. Note: not implemented.

Specified by:

parse in interface ElemFactory<C extends RingElem<C>>

Parameters:

s - String.

Returns:

power series from s.

parse

public MultiVarPowerSeries<C> parse(java.io.Reader r)

Parse a power series. Note: not implemented.

Specified by:

parse in interface ElemFactory<C extends RingElem<C>>

Parameters:

r - Reader.

Returns:

next power series from r.

seriesOfTaylor

public MultiVarPowerSeries<C> seriesOfTaylor(TaylorFunction<C> f,
                                             java.util.List<C> a)

Taylor power series.

Parameters:

f - function.

a - expansion point.

Returns:

Taylor series of f.